Abstract
Let k ≥ 3, θ a nontrivial equivalence relation on E k = {0, . . . ,k – 1}, and ρ a binary central relation on E k (a reflexive graph with a vertex having E k as its neighborhood). It is known that the clones Pol θ and Pol ρ (of operations on E k preserving θ and ρ, respectively) are maximal clones; i.e., covered by the largest clone in the inclusion-ordered lattice of clones on E k . In this paper, we give the classification of all binary central relations ρ on E k such that the clone Pol θ ∩ Pol ρ is maximal in Pol θ.
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Presented by A. Szendrei.
This research was done during a ten month stay of the first author at the University of Montreal. The financial assistance of AUF (Agence Universitaire de la Francophonie) is gratefully acknowledged. The first author thanks Professor Ivo G. Rosenberg and the Department of Mathematics and Statistics at University of Montreal for their hospitality during his visit.
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Temgoua, E.R.A., Rosenberg, I.G. Binary central relations and submaximal clones determined by nontrivial equivalence relations. Algebra Univers. 67, 299–311 (2012). https://doi.org/10.1007/s00012-012-0183-2
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DOI: https://doi.org/10.1007/s00012-012-0183-2